"Who hasn't overheard a conversation between a couple?" Drake Doremus grins. "Who hasn't been a voyeur in certain situations?" From an older man, these words might sound sleazy, but coming from this fuzzy-faced 28-year-old, it sounds playful. After cutting his teeth two years ago on a cheap indie road movie called Douchebag, this Californian director has moved on to a more considered study of young love, becoming an overnight indie star at the 2011 Sundance festival with a film that puts the audience, often unwillingly, right in the heart of the action.

Called Like Crazy, it stars Felicity Jones as a British girl who meets an American boy (Anton Yelchin) in college, beginning a to-and-fro transatlantic affair that will both thrill and thwart them as they try to make it work. "It came about," explains Doremus, "because I had gone through a long-distance relationship myself, and I wanted to explore a lot of the feelings that I'd felt. Now, she wasn't actually British, but I spent a lot of time going back and forth between LA and London in that relationship because she was living there. So to make the character British seemed like a no-brainer."

Though the story's slight, what makes the movie remarkable is the level of closeness that Doremus creates around his two leads. It seems at first sight to be about very little, but over time the minutiae become fascinating, like a live-action version of Robert Doisneau's famous 1950 photograph of a couple kissing by the Hotel De Ville. "I really wanted to make a film that felt intimate to the point that it's so intimate, it doesn't belong to the audience," Doremus says. "I wanted them to feel uncomfortable about what they're watching. The movie that does that really well, that the style in my movie is something of an homage to, is Alfonso Cuarón's Y Tu Mamá También, where the camera floats in and out of intimacy and into voyeurism. The two things create this juxtaposition of feeling very connected emotionally with the characters and also feeling, like, 'Jeez, should we look away now?'"

To achieve this effect, Doremus used a style of improvisation more connected with Brits such as Mike Leigh and Ken Loach than the US indie world. "We started with a 50-page outline," he says, "which was very specific. It had a lot of backstory, a lot of scene objectives, subtext, plot points, emotional beats and things. The only thing it didn't have was actual dialogue, because that sort of thing comes later, after we've understood the objectives and we know where we're going emotionally in the scene. And it keeps the scenes fresh, spontaneous and alive; and therefore they hopefully resonate more, because they feel more real."

'Improv was always in my bones. Anything that's intended to be comedic is something I spent 15 years learning about'

The most surprising thing about Doremus, as he discusses his "process", is how much he smiles while he's at it, with affection rather than po-faced reverence. He's not a disciple of realism for its own sake; neither is he from the shambolic, guerilla school of film-making known as mumblecore. "Everything you see in the film we had permits for, but it's all made to look stolen," he says.

But then, it's maybe not that surprising, given that Doremus's roots lie in comedy. His mother, Cherie Kerr, co-founded LA comedy troupe the Groundlings, which gave the world Will Ferrell, Lisa Kudrow and Kirsten Wiig. "I grew up in that world, from when I was six, then I started performing improv, and eventually teaching it. It was always in my bones. Anything that's intended to be comedic, or have a joke, is something that for 15 years I was learning about." A stint at the American Film Institute taught Doremus about "normal" film-making; he credits that with helping him learn "how to break the rules".

Right now, Doremus is finishing his third movie, another relationship drama starring Guy Pearce and Felicity Jones. He marvels at the way his budgets have spiralled – tenfold from Douchebag's $25,000 to Like Crazy's $250,000 alone – and credits his producer's faith for bringing in seven figures the third time round to rope in a relatively stellar cast. "It's an unrequited love story between an older man and a younger woman who find a connection at a really bad time," he explains. "And the movie's about them navigating those emotions and those feelings."

Is it part of a series; a long-term study of the human heart? "Strangely no," he shrugs. "I get an idea, I wanna make it, and within six months I do it. But I don't have ideas all the time. Like Crazy was a lightning bolt; I was like, 'OK, that's a movie I have to make, and I have to make it in three months.' But I don't have constant ideas, and I worry about that. Because one day the well may dry up ..."